mechanics

MECHANICS REVIEWER

1. The magnitude of the x and y –components of the 2-kN force is A) Fx = -4.00 kN, Fy = -2.31 kN B) Fx = -1.732 kN, Fy = -1.000 kN C) Fx = -1.000 kN, Fy = -1.732 kN D) Fx = -1.414 kN, Fy = -1.414 kN Fig 1 2. The gusset plate G of a bridge joint is subjected to the two member forces at A and B. If the force at B is

horizontal and the force at A is directed at = 30°, determine the magnitude and direction of the resultant force.

A) R = 252 N, = 97.5°

B) R = 458 N, = 97.5°

C) R = 252 N, = 82.5°

D) R = 458 N, = 82.5° Fig 2 3. If expressed in unit vector notation, F is equal to y 400N

A) (400 sin 40⁰ + 400 cos40⁰ )N

B) (400 cos 40⁰ + 400 sin 40⁰ ) N 40⁰

C) (400 cos 40⁰ - 400 cos 40⁰ ) N Fig 3 x

D) (400 sin 40⁰ - 400 cos40⁰ )

4. The dot product of two vectors results in a _________ quantity A)scalar B) vector C)complex D) zero

5. The magnitude of vector C ( = 4 - 3 + ) is

A)zero B)2 C) D)

6. A rectangular system is said to be right-handed if A)the thumb of the right hand points in the direction of the positive z axis when the right hand fingers are curled about this axis and directed from the +x towards the +y axis. B)the thumb of the right hand points in the direction of the negative z axis when the right hand fingers are curled about this axis and directed from the +x towards the +y axis. C) the thumb of the right hand points in the direction of the positive z axis when the right hand fingers are curled about this axis and directed from the -x towards the +y axis. D) the thumb of the right hand points in the direction of the positive z axis when the right hand fingers are curled about this axis and directed from the +x towards the -y axis. z

7. If expressed in Cartesian vector form, F1 is A) (2.50 i + 3.54 j + 2.50 k) kN B) (4.33 i + 3.54 j + 4.33 k) kN C) (4.33 i + 3.75 j + 2.17 k) kN Fig 7

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D) (2.17 i + 3.75 j + 4.33 k) kN

8. The magnitude and direction of the moment of the force of the movement if the force at A about point P.

A) Mp = 400 Nm

B) Mp = 200 Nm

C) Mp = 200 Nm Fig 8

D) Mp = 400 Nm 9. Two points in 3 – D space have coordinates of P (1, 2, 3) and Q (4, 5, 6) meters. The position vector rQP is

given by A) {3 i + 3 j + 3 k} m B) {- 3 i – 3 j – 3 k} m C) {5 i + 7 j + 9 k} m D) {- 3 i + 3 j + 3 k} m 10. The magnitude and direction of the couple moment is A) M = 3120 lb-ft CW B) M = 3120 lb-ft CCW C) M = 3900 lb-ft CW D) M = 3900 lb-ft CCW

Fig 10

11. The triple scalar product u • ( r F ) results in A) zero B) a vector quantity. C) a scalar quantity ( + or - ). D) a unit vector.

12. A general system of forces and couple moments acting on a rigid body can be reduced to a ___ .

A) single force. B) single moment. C) single force and two moments. D) single force and a single moment.

13. Using this FBD, you find that FBC = – 500 N. Member BC must be in __________.

A) tension B) compression C) cannot be determined Fig 13

14. Find the dot product of the two vectors P and Q. P = {3 i + 2 j + 3 k} m; Q = {-2 i + 2 j + 4 k} m A) -10 m B) 10 m

C) 10 m

2 D) -10 m

2

15. The correct FBD of the figure is

A) B) C) D) θ θ θ θ

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Fig 15 16. If the support is a rocker, in drawing the free-body diagram, the reaction force has _ unknown(s)

A) 1 B) 2 C) 3 D) 4

17. Which equation of equilibrium allows you to determine FB right away?

A) FX = 0

B) FY = 0

C) MA = 0 Fig 17 D) Any one of the above

18. To determine Fr in the figure, we use

A) Cosine law B) Sine Law C) Pythagorean Theorem D) None of these Fig 18 19. F in unit vector notation in figure 19 is A) 100i N B) 100j N C) -100i N D) -100j N Fig.19 20. The magnitude of Fr in Figure 20 is A) 250N B) -500N C) 500N D) -250N Fig. 20

21. The y-component of the 100N force is A) 100N sin45⁰ sin 60⁰ B) 100N sin45⁰ cos 60⁰ C) 100N cos45⁰ cos 60⁰ D) 100N cos45⁰ sin 60⁰ Fig 21

22. A force of 100N acts at point A .The value Fig 22 of FAC is

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A) 70.71 N B) 100N C)141.4N D) 0 N

23. The moment of 100-N force about O is A) (70.7k) Nm B) (141.4k) Nm C) (-141.4k) Nm D) (-70.7k) Nm Fig 23 24. The equivalent force and couple moment system acting at A is A) (-100i)N, (100k)Nm B) (100i)N, (-100k)Nm C) (100j)N, (100k)Nm Fig 24 D) (100i)N, (100k)Nm 25.In figure 25, is the rod a two- force member? Fig 25 A) Yes B) No

26. In the method of joints, typically _________ equations of equilibrium are applied at every joint. A) two B) three C) four D) six

27. If the numbers of unknown forces is more than the equations that can be used, the system is said to be A) statically determinate B) statically undeterminate C) statically indeterminate

D) statically deformed 28. The position vector is represented by A) (-2i - 4j + 3k) m B) (3i + 4j) m C) (4j + 3k) m D) (2i + 4j + 4k) m Fig 28 29. If the support is a rocker, in drawing the free-body diagram, the reaction force has _ unknown(s) A) 1 B) 2 C) 3 D) 4

30. Fr can be determined by A) Sine law B) Cosine law C) Pythagorean Theorem Fig 30

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1. Given: figure 1 as shown, the horizontal component of 400N force is A) 400N cos 30° B) 400N sin 30° C) -400N cos 30° D) -400N sin 30° Fig. 1 2. In figure 1, the vertical component of 250N force is

A) 250N B) 250N C)250N D) 250N

3. The resultant of the three forces in figure 1 is A) 896N, 38.9⁰ B) 638N, 51.1⁰ C) 896N, 51.1⁰ D) 638N, 38.9⁰ 4. Engineering mechanics is formulated on the basis of Newton’s A)First Law B)Second Law C)Third Law D)three laws of motion 5. Force F as a cartesian vector in figure 5 is

A) lb.

B) lb.

C) lb.

D) lb. Fig 5 6. If the magnitude of F is 80N, and 45⁰, the magnitude of its component is A) Fx = 138.6N , Fy= 80.0N, Fz = 58.6N B) Fx = 40.0N , Fy= 80.0N, Fz = 58.6N C) Fx = 40.0N , Fy= 56.6N, Fz = 40.0N Fig 6 D) Fx = 80.0N , Fy= 80.0N, Fz = 58.6N 7. The moment of the force at A about point P is

A) Mp = 33.5 kN-m

B) Mp = 33.5 kN-m

C) Mp = 18.48 kN-m Fig 11

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D) Mp = 33.5 kN-m

8. The triple scalar product u • ( r F ) results in A) zero B) a vector quantity. C) a scalar quantity ( + or - ). D) a unit vector

1. If x = 3t3 m, where t is in seconds, the particle’s velocity when t = 2s is A)6 m/s B)18 m/s C)24 m/s D)36.0 m/s 2. Given: the v-t graph, the acceleration of the particle when t= 3s is A) 5.00 m/s2

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B) 15.00 m/s2 C) -5.00 m/s2

D)27.5 m/s2 3. A particle P is traveling around a circular path such that at the instant considered, the

speed is 3m/s and increasing at 4 m/s2. The magnitude of the particle’s acceleration at that instant is A) 0 m/s2

B) 3.00 m/s2 C) 4.00 m/s2 D) 5.00 m/s2 4. A ball is thrown horizontally from A with a speed of vA= 6 m/s. If it strikes the ground

in t = 1.52 s, the height h is A) 11.33m B) 3.95 m C) 8.91 m D) 9.12 m

6. At a given instant, blocks A and B have the motion shown. The acceleration of

block B with respect to A is A) 2i m/s2

B) 1i m/s2 C)-1i m/s2

D) 3i m/s2 7. If the end of the cable at A is pulled down

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at a speed of 2 m/s.The speed with which block B rises is A) – 2 m/s B) 2m/s C) 1 m/s D) -1 m/s

8. In polar coordinate, the radial acceleration is defined as

A) B) C) + D) E) 9. In the figure, which equation relates the position of the blocks? A) xA + xB + xC = L B) 2xA + xB + xC = L C) xA + xB + 2xC = L D) xA + 2xB + xC = L

10. A stone is thrown vertically upward and returns to earth in 10 sec. What was its initial velocity? A) 9.81 m/s B) 98.1 m/s C) 161 ft/s D) 37.2 ft/s

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1 The free-body diagram of the rod is shown in the figure. What equation represents the moment about point A? A) -200N(4m) + F(2m) = 0 B) -20N(4cos30

om) + F(2m) = 0

C) -200N(4cos30om) + F(2m) = 0

D) -200N(4m) +Fcos30(2m) = 0

2. The magnitude of the couple shown is A) 1200N-m CW B) 1200N-m CCW C) 800N-m CW D) 400 N-m CCW 3. The moment of a force about an axis is obtained by forming the mixed triple

product of B) C) D)

4. The frictional effects of the air on the blades of the standing fan creates a couple moment of Mo = 6 N-m on the blades. The value of couple forces at the base of the fan so that the resultant couple moment on the fan is zero is A) 40N B)20N C) 80N D) 1.8N

5. The maximum number of unknowns for three-dimensional rigid body is A) 3 B) 4 C)5 D)6 6. Which of the following is FALSE? A) A couple moment is produced by two noncollinear forces which are equal in

magnitude but opposite in direction. B) A couple moment causes different effect of rotation on a body when it is applied at

different points C) A resultant couple moment is simply the vector sum of all the couple moments of

the system.

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D) The forces exerted by your hand on a screw-driver is an example of a force-couple system.

7. The moment of the couple's two forces about point A is A) 100 N-m clockwise B) 200 N-m clockwise C) 250 N-m clockwise D) 300 N-m clockwise

8. The magnitude of F for each of the two forces acting on the outer circle, so that they create the same couple moment as that created by the 100-N forces acting on the inner circle is

A) 10 N B) 25 N C) 40 N D) 80 N

9. If the numbers of unknown forces is more than the equations that can be used, the

system is said to be A) statically determinate B) statically undeterminate C) statically indeterminate D) statically deformed

10. If the support is a rocker, in drawing the free-body diagram, the reaction force has _ unknown(s) A) 1 B) 2 C) 3 D) 4

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1. If the Modulus of Elasticity of wood is 2 x106 psi and the modulus of elasticity of brass is 15 x 106 psi, which of the two materials is most likely to be transformed to another material to find the allowable stress.

A) wood B) brass

2. For reinforced concrete beams, A) steel is transformed into concrete to find the neutral axis B) concrete is transformed into steel to find the neutral axis C) The area of the concrete is multiplied by n D) the neutral axis can be solved by linear equation.

3. In the method of joints, typically _________ equations of equilibrium are applied at every joint.

A) two B) three C) four D) six

2. The sum of the vertical forces in figure is

A)

B)

C)

D)

Fig 4 3. The magnitude of the resultant in figure is A) 103.0 lb B)42.57 lb C)145.62 lb D)111.5 lb

4. If the value of F in fig.4 if 400N, its components are A)346 i +136.8j + 306k B) 346 i + 306j +136.8k C) 136.8 i + 346 j + 306k D) 136.8 i + 306j + 346 k 5. The 120-lb force can be expressed in Cartesian

vector notation as A) (-40i -80j + 40k) lb fig 5 B) (80i -40j + 40k) lb C) (-80i +80j - 40k) lb D) (-80i -80j + 40k) lb

6. The equivalent force in figure is A) -403N i -1006Nj B) -503N i -406Nj C) -189N i -245Nj D) -459N i -735Nj 7. The moment of the couple in figure is fig 6,7,8 A) 975Nm

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B) 760 Nm C) 901 Nm D) 811 Nm 8. The direction of the couple moment in figure is A) clockwise B) counterclockwise

9. Two points in 3 – D space have coordinates of P (1, 2, 3) and Q (4, 5, 6) meters. The position vector rQP is given by

A) {3 i + 3 j + 3 k} m B) {- 3 i – 3 j – 3 k} m C) {5 i + 7 j + 9 k} m D) {- 3 i + 3 j + 3 k} m

10. The magnitude of vector C ( = 5 - 3 + ) is

A)zero B)3 C) D)

12. The magnitude and direction of the moment of the force of the movement if the force at A about point P.

A) Mp = 400 Nm

B) Mp = 200 Nm

C) Mp = 200 Nm fig 12

D) Mp = 400 Nm 13. Find the dot product of the two vectors P and Q. P = {3 i + 2 j + 3 k} m; Q = {-2 i + 2 j + 4 k} m A) -10 m B) 10 m

C) 10 m

2 D) -10 m

2

14. From the free body diagram shown in the figure, select the equation that represents the moment about A fig.14

A)

B)

C)

D)

15. Is member AB a two-force body? A) Yes B) No fig 15

16. A force of 150N acts at point A .The value Fig 22 of FAC is

A) 106.1 N B) 150N C)212N D) 0 N fig 16

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17. The cross product of B and A , that is ( in the figure is

A) positive

B) negative

Fig 17 18. In the method of joints, the number of equations that can be applied at each joint is

A) two B) three C) four D) six

20. If the force in each member of the whole truss is asked, we use method of___ A) sections B)dismember c)joints D) supports

Fig 22

22. Using this FBD, you find that FBA = – 300 N. Member BA must be in __________.

A) tension B) compression C) cannot be determined

23. To determine Fr in the figure, we use A) Cosine law B) Sine Law C) Pythagorean Theorem fig 23, 24 D) None of these 24. The magnitude of Fr in fig. is A) 146.4 N B) 273 N C) 245 N D) 179.3 N

25. Can you determine the force in member DC by making the cut at section a-a? Explain your answer.

A) Yes, using MD = 0 .

B) Yes, using ME = 0 .

C) Yes, using MB = 0 . fig 25 D) No, there are 4 unknowns.

26. The y-component of the 200N force is A) 200N sin45⁰ sin 60⁰ B) 200N sin45⁰ cos 60⁰ C) 200N cos45⁰ cos 60⁰

D) 200N cos45⁰ sin 60⁰ fig 26

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27. A general system of forces and couple moments acting on a rigid body can be reduced to a ___ . A) single force. B) single moment. C) single force and two moments. D) single force and a single moment.

28. As shown, a cut is made through members GH, BG and BC to determine the forces in them. Which section will you choose for analysis and why?

A) Right, fewer calculations. B) Left, fewer calculations. C) Either right or left, same amount of work. Fig 28 D) None of the above, too many unknowns.

29. The number of unknowns in member AB is A)2 B)3 C)4 D)1 Fig 29

30. The moment of the force about point O using the vector cross product is

A) (20i - 30k) Nm B) (60i - 30k) Nm C) (60i - 30j) Nm D) (60i + 40j - 30k) Nm fig 30

3.The hollow member has a square cross section with outer length of side equal to 50 mm and inner length of side equal to 35 mm. If a force of 10 kN is acting on it. The required cross sectional area is A) .015m4 B)2.83 x 10-3m4 C)1.275 x 10-3m2 D)3.65 x 10-3m4 4. The normal stress it has is

10 KN A) .667 MPa B)3.53 MPa C) 2.74 MPa D)7.84MPa Fig 3,4,&5

5. The normal stress it has if the member is solid is A)4.00 MPa B) 8.16 MPa C)5.34 MPa D)2.31 MPa 6.An 8-mm diameter brass rod has a modulus of Elasticity of Ebr= 100 GPa. If it is 3m long and subjected to an axial load of 2.0 kN, its elongation is

A)0.838mm B)1.193mm C)2.39mm D).419mm Fig 10& 11

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7. If the diameter in the figure is 6mm, its elongation under the same load is A) The same B)4.24 mm C)2.12 mm D)1.06 mm

8. In torsion, as the shaft is subjected to a torsional load, the square element deforms into A)rectangle B) rhombus C) circle D) triangle

9.Determine the largest allowable diameter of a 3-m long steel rod(G= 77 GPa) if the rod is to be twisted through 30⁰, without exceeding a shearing stress of 84 MPa.

A) 12.50mm B) 6.00 mm C)7.05 mm D) 15.00 mm

17. If the direction of the bending moment is the same as in the figure shown, there will be

A) tension above the neutral axis of the beam B) compression below the neutral axis of the beam C) tension along the neutral axis

D)compression above the neutral axis of the beam M M

18. A tubular shaft, having an inner diameter of 30 mm and an outer diameter of 42 mm, is to be used to transmit 90 kW of power. Determine the frequency of rotation of the shaft so that the shear stress will not exceed 50 MPa. A)167.3 Hz B) 26.6 Hz C) 538 Hz D)727 Hz 19. For reinforced concrete beams,

A) steel is transformed into concrete to find the neutral axis B) concrete is transformed into steel to find the neutral axis C) The area of the concrete is multiplied by n D) the neutral axis can be solved by linear equation.

20. In the figure, the torque acting on AB is A) 1600 Nm, CW B) 400 Nm, CCW Fig 20 C) 600 Nm, CW D) 600 Nm, CCW 21. A steel shaft 3 ft long that has a diameter of 4 in. is subjected to a torque of 15 kips-ft. If G= 12 x 106 psi, the maximum shearing stress is A) 14.32 ksi B) 13.42 ksi C) 1432 psi D)1342 psi

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1. The block has a mass m and given an initial velocity vO up the plane. What is the friction force

between the block and the plane. The coefficients of static and kinetic friction between the block and

the plane are μs and μk respectively.

a. μsmg sinθ

b. μsmg cosθ

c. μkmg sinθ

d. μkmg cosθ

2. Determine the acceleration of the block when the block weighs 5 kg, P = 60 N

and θ = 30⁰.

a. 2.20 m/s2 upward

b. 3.17 m/s2

upward

c. 11.0 m/s2 upward

d. 4.26 m/s2 upward

1 This relates displacement, velocity, acceleration and time without reference to the cause of motion. A)Mechanics B)Kinetics C)Kinematics D)Dynamics E)Statics 2 Which of the following is not a curvilinear motion? A)satellite’s motion B)projectile C)a jeepney making a round in a rotunda

D) a rotating disc E)passenger in a turning ferris wheel 3 If a = (2t) m/s2, where t is in seconds, calculate the particle's velocity when t = 2s.

When t = 0, Vo = 2m/s. A) 0 m/s B) 2 m/s C) 4 m/s D) 6 m/s E) 8 m/s

4. If s = (4t2) m, calculate the particle's acceleration at t = 2s. A) 0 m/s2 B ) 4 m/s2 C) 8 m/s2 D) 16 m/s2 E) 32 m/s2 5. The particle shown in the figure travels from A to B in 1s, it then travels from B to C in 1s.

What is the average velocity? A) 1 m/s B) 2 m/s C)-1 m/s D)-5 m/s E)-2 m/s

6. Given the s - t graph. Calculate the particle's velocity when t=1s.

A) 2 m/s B) 0.5 m/s C) 1 m/s D) 4 m/s E)-1 m/s 7. Given the v - t graph. Calculate the particle's acceleration when t = 3s. A) -1.67 m/s2 B) -5 m/s2 C) -10 m/s2 D) -15 m/s2 E) -2.5 m/s2

8. In the figure in number 7, what is the particle’s position at the end of 4s?

A) 30m B) 20m C) 40m D) 10m E)15 m

9. A ball is thrown horizontally from A with a speed of vA = 6m/s as shown. If it strikes the ground

in t = 1s .determine the height h. A) 9.81 m B) 10.90m C)6.00m D) 4.43m E)4.91m

10. The value of R in number 9 is A) 9.81 m B) 10.90m C)6.00m D) 4.43m E)4.91m

11. A ball is thrown at an angle of 45⁰ with the horizontal at an initial speed of VA= 10m/s. What is the

maximum height it can attain? A)2.55 m B)0.722m C)4.91 m D)9.81m E)7.07m

12. When t = 0, s = 0.5, v = 1m/s. If v = (3t + 1) m/s, where t is in seconds, compute the distances traveled by the particle when t = 1s.

A)3.5m B)4.5m C)6m D) 3m E)5m 13. In polar coordinate, the radial acceleration is defined as

A) B) C) + D) E) 14. The normal component of acceleration is

A) B) C) D) E)

15. Select the equation which relates the position of the end of the cable B to the position of block A. A) SB + SA = L B) 2SB + SA = L C) SB + 3SA = L D) SB + 2SA = L E) SB + 2SA = 0

18.Newton’s ____ law forms the basis of the study of dynamics. A)1st B)2nd C)3rd D)gravitation E)momentum 19. Determine the work done by the force when it is subjected to the displacement indicated. A)0J B)20.0J C)10.0J D)5.00J E)17.32J

20. The work done by the spring in the figure is A)-50J B)50J C)25J D)100J E)10J

21. A 200kg crate is on top of a 5m –hill. Its potential energy with respect to the bottom of the hill is A) 9.80x103J B)1.000X103J C)5.00X103J D) -9.80x103J E) -1.000X103J 22. I ft-lb is equivalent to _____Joules. A)1 B)746 C)550 D)980 E)1.356 23. In the pendulum bob, kinetic energy is greatest A) at the right end point of its swing B) at the bottom of its swing C) midway between the end point of its swing and the bottom of its swing. D) at all points of its swing E) at the left end point of the swing

24. At the bottom of a loop, the speed of the roller coaster is 587 ft/s. This causes a normal acceleration of 9g ft/s2.The radius of the loop is A)1380 ft B)1188 ft C) 3.90x103 ft D)3.83x104 ft E)552 ft 25. It is convenient to express the velocity and acceleration vectors using radial and transverse components in

A)polar coordinates B)rectangular coordinates C)cylindrical coordinates 26. In projectile motion, acceleration along the y-axis is A)zero B)uniform C)a function of t D)a function of h E)a function of v 27. Given the a-t curve, the change in ______ between t1 and t2 is equal to the area under the a-t curve between t1 and t2.

A)position B)acceleration C)time D)slope E)velocitY

28. Kinetic energy results from

A)displacement B)friction C)gravity D)velocity E)height

29. A stone is dropped from the roof of a building 35m high. It will reach the ground after

A) 0.749s B)2.67s C)1.33s D)1.69s E)1.43s

1 A 10 Kg block rests on a smooth surface, compute the block's initial acceleration.

A) 0 m/s2

B) 2 m/s2

C) 5 m/s2

D) 10 m/s2

2. Calculate the power developed by the 100 N force which acts on the 10 Kg block. The block has a speed of 2 m/s.

A) 50 W B) 100W C)200 W D) 250W

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3. The 10 Kg block is released from rest at A. Select the equation that represents the reduced form of the conservation of energy theorem, necessary to determine the maximum compression h in the spring at B. Place the datum at A. A) 0 = -98.1h - 98.1 - 50h

2

B) 0 = -98.1h + 50h2

C) 0 = -98.1 - 98.1h + 50h2

D) 0 = -98.1 - 50h2

4. The speed of block A if block B has an upward

velocity of 6 ft/s is

A) 12 ft/s ↑

B) 1.5 ft/s ↓

C) 2 ft/s ↓

D) 18 ft/s↓